It is not clear where in human evolution we specifically qualify as in the image of God in the sense of Genesis 1, nor whether that is abrupt or more gradual. Even young-earthers are all over the map when it comes to calling a particular hominid a human versus just an ape.
We also don’t know exactly what physical and social traits would have distinguished Neanderthals or especially Denisovians from modern humans. We have enough Neanderthal skeletons to know the general build but not details like hair pattern. They probably had some speech capacity but would have sounded different.
Judging by modern humans, a very likely scenario for interbreeding would be for a young adult male modern human to go out in search of new opportunities (especially if he had limited opportunities back home) and then reach the conclusion that, if he wanted to get a date, he’d have to go with someone who didn’t look quite like the folks back home. Conversely, a local female might be impressed by the potential of someone with new ideas, even though he looked kind of funny.